Is it permissible to throw away, in the regular trash, dead flowers that were used for Shabbat during the shmita? The flowers were kosher for Shmita but my wife seems to think that they must be composted rather than just throwing them away because it is Shmitta. Also, are there any sources? She won’t believe me w/o a source.

ב"ה Shalom First of all only flowers that have a fragrance are the ones that have "kedushat Shvi'it", flowers that have no fragrance have no kedusha and may be disposed of normally. ספר השמיטה, הרב יחיאל מיכל טוקיצ'ינסקי זצ"ל, פרק ז, ד סק"ה) Some hold that even flowers which have fragrance but are not eaten do not have Kedusha and according to these opinions, surely they may be disposed of normally. ) רב וולדנברג זצ"ל , ציץ אליעזר ח"ו סי' לג,) (See also Rav Yosef Tzvi Rimon's book Shmitta, Hebrew version pg. 199) Furthermore, flowers that are allowed to be sold during Shmitta may have grown in hot houses in flower pots in which the flowers have no contact with the earth and therefore the laws of Shmitta may not apply to them at all. In addition, even flowers which do have kedusha, the requirement is only that they are not tossed with all the trash, but if placed in a separate closed bag, they are not dishonored. Keep up the mitzvah of buying flowers for your wife for Shabbat. All the best